{"query": "If Sha is finite, the rank is computable", "count": 15, "results": [{"id": "card_joint_manin_algorithm", "title": "If Sha is finite, the rank is computable", "shelf": "codex", "surface": "secular", "snippet": "Manin (1971): if the Tate-Shafarevich group is finite - part of what BSD asserts - then the rank of an elliptic curve over Q is effectively computable by descent. Without it, no algorithm is known. A ", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "readable": false, "generated": false}, {"id": "card_theory_digital_analog", "title": "Digital versus analog (why discreteness survives copying)", "shelf": "theories", "surface": "secular", "snippet": "Digital versus analog (why discreteness survives copying) — an engine domain that can touch it: computer_science. Calibration: map-only — sampling rates and bit depth are ordinary arithmetic, and THIS", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_church_turing_thesis_computability", "title": "Church–Turing thesis / computability", "shelf": "theories", "surface": "secular", "snippet": "Church–Turing thesis / computability — an engine domain that can touch it: computer_science. Calibration: map-only — a thesis, not a theorem. Everything effectively computable is computable by a Turin", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_numerical_analysis", "title": "Numerical analysis (why the computer's answer is not the answer)", "shelf": "theories", "surface": "secular", "snippet": "Numerical analysis (why the computer's answer is not the answer) — an engine domain that can touch it: computer_science. Calibration: map-only — error bounds and condition numbers are computable in pr", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_src_etym_computable", "title": "computable", "shelf": "etymology", "surface": "secular", "snippet": "computable: etymology (Webster 1913) — a.: [L. computabilis.]. From Webster's Revised Unabridged Dictionary (1913), public domain.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_src_mill_manin_1971", "title": "Yu. I. Manin 1971 — Cyclotomic fields and modular curves", "shelf": "millennium", "surface": "secular", "snippet": "Yu. I. Manin (1971). Cyclotomic fields and modular curves. Russian Math. Surveys 26:6 (1971) 7–78. DOI 10.1070/RM1971v026n06ABEH001272. Canonical: https://doi.org/10.1070/RM1971v026n06ABEH001272. No f", "authority_tier": "reference", "source": "Yu. I. Manin (1971), Russian Math. Surveys 26:6 (1971) 7–78", "readable": false, "generated": false}, {"id": "card_chain_turing_1936", "title": "Turing 1936 — On computable numbers, with an application to the Entscheidungsproblem", "shelf": "codex", "surface": "secular", "snippet": "A. M. Turing (1936). On computable numbers, with an application to the Entscheidungsproblem. Proc. London Math. Soc. (2) 42 (1937) 230–265. DOI 10.1112/plms/s2-42.1.230. Canonical: https://doi.org/10.", "authority_tier": "reference", "source": "A. M. Turing (1936), Proc. London Math. Soc. (2) 42 (1937) 230–265", "readable": false, "generated": false}, {"id": "card_src_mill_silverman_1988", "title": "J. H. Silverman 1988 — Computing heights on elliptic curves", "shelf": "millennium", "surface": "secular", "snippet": "J. H. Silverman (1988). Computing heights on elliptic curves. Math. Comp. 51 (1988) 339–358. DOI 10.1090/S0025-5718-1988-0942161-4. Canonical: https://doi.org/10.1090/S0025-5718-1988-0942161-4. Free c", "authority_tier": "reference", "source": "J. H. Silverman (1988), Math. Comp. 51 (1988) 339–358", "readable": false, "generated": false}, {"id": "card_builder_gottfried_wilhelm_leibniz", "title": "Gottfried Wilhelm Leibniz", "shelf": "builders", "surface": "secular", "snippet": "Gottfried Wilhelm Leibniz (1646–1716 AD) — mathematics. The gift: the calculus (independently, with the notation we still use), binary arithmetic, and the dream of a universal calculus of reasoning. W", "authority_tier": "reference", "source": "The builders of the Floor — credited with love, calibrated to the plumb-line", "readable": false, "generated": false}, {"id": "card_calc_black_scholes", "title": "Black-Scholes equation", "shelf": "calculations", "surface": "secular", "snippet": "Black-Scholes equation — finance. Formula: dV/dt + rS dV/dS + sigma^2 S^2/2 d2V/dS2 = rV. Canonical FORM: diffusion (du/dt = D * laplacian(u)) — an option price diffuses — the heat equation in disguis", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_kimura_diffusion", "title": "Kimura allele diffusion", "shelf": "calculations", "surface": "secular", "snippet": "Kimura allele diffusion — biology. Formula: dp/dt = drift + (1/2)V d2p/dp^2. Canonical FORM: diffusion (du/dt = D * laplacian(u)) — allele frequencies drift and diffuse in a finite population — the di", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_src_etym_estimable", "title": "estimable", "shelf": "etymology", "surface": "secular", "snippet": "estimable: etymology (Webster 1913) — a.: [F. estimable, or L. aestimabilis. See Esteem.]. From Webster's Revised Unabridged Dictionary (1913), public domain.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_src_word_estimable", "title": "estimable", "shelf": "dictionary", "surface": "secular", "snippet": "estimable: (adjective) deserving of respect or high regard · (adjective) deserving of esteem and respect — syn: good, honorable, respectable · (adjective) may be computed or estimated — syn: computabl", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_pron_estimable", "title": "estimable", "shelf": "pronunciation", "surface": "secular", "snippet": "estimable: pronounced (ARPABET) EH1 S T AH0 M AH0 B AH0 L. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "readable": false, "generated": false}, {"id": "card_src_word_computable", "title": "computable", "shelf": "dictionary", "surface": "secular", "snippet": "computable: (adjective) may be computed or estimated — syn: estimable", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_joint_manin_algorithm"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}